This looks very like trying to define away something that sure felt like a paradigm shift to the people in the field. Remember that “paradigm” is a belief held by people, not a property inherent in the universe.
Perhaps this is a limitation of my understanding of Kuhn, in that I’m misusing his terminology. I am unaware of mathematics abandoning fundamental objects as inherently misguided the way physics abandoned epicycles or impetus. I expect physics will have similar abandonments in the future, but I expect mathematics never will. The difference is a property of the difference between mathematics and empirical facts. This comment makes the argument I’m trying to assert in slightly different form.
This looks very like trying to define away something that sure felt like a paradigm shift to the people in the field. Remember that “paradigm” is a belief held by people, not a property inherent in the universe.
Perhaps this is a limitation of my understanding of Kuhn, in that I’m misusing his terminology. I am unaware of mathematics abandoning fundamental objects as inherently misguided the way physics abandoned epicycles or impetus. I expect physics will have similar abandonments in the future, but I expect mathematics never will. The difference is a property of the difference between mathematics and empirical facts. This comment makes the argument I’m trying to assert in slightly different form.